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Ajutati-ma va rog ....3{x}-[x]=1/4

Răspuns :

3{x}-[x]=1/43(x-[x])-[x]=1/4
3x-3[x]-[x]=1/4
3x-4[x]=1/4
4[x]=3x-1/4
[x]=3x/4-1/16
[x]=(12x-1)/16=k∈Z
12k-1=16k
x=(16k+1)/12
Din [x]=k=>
k≤x<k+1
k≤(16k+1)/12<k+1 | ·12
12k≤16k+1<12k+12  |-12k
0≤4k+1<12 |-1
-1≤4k<11 | :4
-1/4≤k<11/4 si k∈Z
k∈{0,1,2}
Daca k=0 =>x=(16k+1)/12=1/12.
Daca k=1 =>x=(16k+1)/12=17/12.
Daca k=2 =>x=(16k+1)/12=33/12.